While the Progressive Era was very important, most of the progressive actions were taken by the Democratic and Republican Parties. The Progressive Party (better known as the Bull Moose Party) was not very important. In fact, its main importance comes from the fact that its existence allowed Woodrow Wilson to win the presidential election of 1912.
In 1912, Theodore Roosevelt lost in his attempt to supplant President Taft as the Republican nominee for president. When this happened, he and others created the Progressive Party. The presence of Roosevelt and the Progressive Party split the Republican vote in the election and allowed Wilson to win with 42% of the popular vote.